Position of the median in ordered data?

The \frac{n+1}{2}th value; for even n, the mean of the two middle values.

The most frequent value (or the modal class for grouped data).

Why is a grouped mean only an estimate?

Individual values are unknown, so the midpoint is used for every value in a class.

Modal class when class widths are unequal?

The class with the highest frequency density, \frac{f}{w}.

How do you combine the means of two samples?

\bar x=\frac{n1\bar x1+n2\bar x2}{n1+n2} (use totals, not an average of means)

Which measure of location is best for skewed data, and why?

The median, because it is not affected by extreme values.

Measures of locationEdexcel International A Level Maths: Flashcards

Card 1 of 130 of 13 known

Question

Formula for the mean of ungrouped data?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

Formula for the mean of ungrouped data?: $\bar x=\frac{\sum x}{n}$
Formula for the mean from a frequency table?: $\bar x=\frac{\sum fx}{\sum f}$
Position of the median in ordered data?: The $\frac{n+1}{2}$ th value; for even $n$ , the mean of the two middle values.
What is the mode?: The most frequent value (or the modal class for grouped data).
What is used for $x$ when estimating a grouped mean?: The midpoint of each class.
Why is a grouped mean only an estimate?: Individual values are unknown, so the midpoint is used for every value in a class.
Formula for the median of grouped data by interpolation?: $L+\frac{\frac n2-F}{f}\times w$
Modal class when class widths are unequal?: The class with the highest frequency density, $\frac{f}{w}$ .
If $y=\frac{x-a}{b}$ , how do you find $\bar x$ from $\bar y$ ?: $\bar x=b\bar y+a$
How do you combine the means of two samples?: $\bar x=\frac{n_1\bar x_1+n_2\bar x_2}{n_1+n_2}$ (use totals, not an average of means)
Which measure of location is best for skewed data, and why?: The median, because it is not affected by extreme values.
Which measure of location can be used for non-numerical data?: The mode.
Which measure of location is affected most by an extreme value?: The mean.

Exam questions on Measures of location

A hockey team scored the following numbers of goals in its first 10 matches of a season: 0, 1, 1, 2, 2, 2, 3, 3, 4, 6.
The team plays two more matches. The mean number of goals per match over all 12 matches is then 2.5. Find the total number of goals scored in the two extra matches.2 marks
The times, in minutes, taken by 40 students to complete a puzzle are summarised as follows: 0 to under 10 minutes, 4 students; 10 to under 20 minutes, 10 students; 20 to under 30 minutes, 16 students; 30 to under 50 minutes, 10 students. Assume that times are spread evenly within each class.
Use linear interpolation to estimate the median time.2 marks
The masses, $m$ grams, of a sample of 20 packets of rice are coded using $y=\frac{m-500}{10}$ . It is given that $\sum y=36$ .
Find the mean mass of the 20 packets.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).